Related papers: Symplectic tracking through curved three dimension…

We present a multiscale integrator for Hamiltonian systems with slowly varying quadratic stiff potentials that uses coarse timesteps (analogous to what the impulse method uses for constant quadratic stiff potentials). This method is based…

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the…

Computing the trajectories of particles in generic beamlines is an important ingredient of experimental particle physics, in particular regarding near-beam detectors. A new tool, Hector, has been built for such calculations, using the…

This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…

We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…

This paper had no abstract originally. A second-order symplectic integration algorithm for guiding center motion is presented. The algorithm is based on the Poincar\'e (mid-point) generating function.

Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…

Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…

We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…

The kinetic term of the $N$-body Hamiltonian system defined on the surface of the sphere is non-separable. As a result, standard explicit symplectic integrators are inapplicable. We exploit an underlying hierarchy in the structure of the…

The symplectic projector method is applied to derive the local physical degrees of freedom of a particle moving freely on an arbitrary surface. The dependence of the projector on the coordinates and momenta of the particle is discussed.

As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. After surveying some of the most important ways of measuring the size of a symplectic set, these…

We study two-dimensional conformal field theories generated from a ``symplectic fermion'' - a free two-component fermion field of spin one - and construct the maximal local supersymmetric conformal field theory generated from it. This…

Multi-symplectic integrators are typically regarded as a discretization of the Hamiltonian partial differential equations. This is due to the fact that, for generic finite-dimensional Hamiltonian systems, there exists only one independent…

Topolectrical circuits provide a versatile platform for exploring and simulating modern physical models. However, existing approaches suffer from incomplete programmability and ineffective feature prediction and control mechanisms,…

We construct a multiplicative spectral sequence converging to the symplectic cohomology ring of any affine variety $X$, with first page built out of topological invariants associated to strata of any fixed normal crossings compactification…

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…

We present a framework based on Clarke coordinates for spatial displacement-actuated continuum robots with an arbitrary number of joints. This framework consists of three modular components, i.e., a planner, trajectory generator, and…

The appearance of tracks, close to classical orbits, left by charged quantum particles propagating inside a detector, such as a cavity periodically illuminated by light pulses, is studied for a family of idealized models. In the…

Formation flight of unmanned aerial vehicles (UAVs) poses significant challenges in terms of safety and formation keeping, particularly in cluttered environments. However, existing methods often struggle to simultaneously satisfy these two…